Q1:Let U = {1, 2, 3, 4, 5},                                   C = {1, 3}   and A and B are non empty sets. Find A in each of the following: (i) A ∪ B = U, A ∩ B = φ and B = {1} (ii) A ⊂ B and A ∪ B = {4, 5} (iii) A ∩ B = {3}, A ∪ B = {2, 3, 4} and B ∪ C = {1,2,3}

Q: 12] and a3 = -20 4 -------- Let a₁ = h 5 2 The set {a1, a2, a3} will span R³ unless h = 0

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Q: 11. For sets A and B, define AAB (A\B) U (B\A). Prove that A B if and only if AAB=0. - (a) Let A and…

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Q: State whether the following claim is true and explain why. (a) Claim: For all sets A, B, and C: (A –…

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Q: Q1 Let U : Determine the following. {1, 2, 3} be the universal set and let A = (1, 2}, B = (2, 3}…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Prove: For all sets A, B and C, (AUB) - (CA) = AU (B-C).

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Q: a) Suppose A, B and C are sets. What do you need to show to prove the following using the definition…

A: Definition : A⊂B iff (x∈A⇒x∈B)WLOG : Without Loss Of Generality.

Q: Let A, B, and C be sets. Prove (AUB)NC= (ANC) U(BNC)

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Q: 4. For the four pairs of sets below, determine whether or not they are equipollent. i.) {2, 5, 10}…

A: We have to check the given sets are equipollent or not.

Q: Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that(i) A × (B ∩ C) = (A ×…

A: i) Answer(i) A × (B ∩ C) = (A × B) ∩ (A × C) (proved)

Q: Let S1= {1, 5, 10, 15, 20} and let S2 = {1, 2, 3, 4, 5}. What is: (a) S1 ∪ S2 (b) S1 ∩ S2 (c) S1 –…

A: Given: The given sets are S1=1, 5, 10, 15, 20 and S2=1, 2, 3, 4, 5. To find: The main aim is to find…

Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: (a) Let A, B be sets. Prove that A\(An B) = A\B. You may assume all sets in the question are…

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Q: a) Let A = {4, 7, 8} and B = {−1, 5}, Find and compare sup(A+B) , inf(A+B), sup(A)+sup(B),sup A -…

A: See the attachment

Q: set identities that A∪B∪ (A∩B∩C) = A∪B∪C

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Q: 9. Which of the following are true for all sets A, B, and C. If the statement is true, prove it by…

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Q: For the four pairs of sets below, determine whether or not they are equipollent. i.) {2, 5, 10} and…

A: We have to find the equipollnt sets from the given pair of four sets.

Q: Does A − (B − C) = (A − B) ∪ C hold for all sets A, B, and C? Prove or give a counterexample for…

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Q: Let A, B and C be arbitrary sets. Does it always hold that A ∪ (B × C) = (A ∪ B) × (A ∪ C) ?

A: No, this is not true in general. For example, consider the following :

Q: But change the problem to say A={1,5,7,11}, B={3,5,7}, C={3,7,9,11}

A: The union of two sets contains all the elements contained in either set (or both sets).The union is…

Q: How many subsets are there for the set {h, j}?

A: The given set is {h, j}.It is known that, “If a set contains ‘m’ elements, then the number of…

Q: Let A, B and C be sets. Consider the following statements. Which of them are true? 1. Ax B = B×A 2.…

A: Given that A, B and C are sets. Note: According to Bartleby guidelines we can solve only first three…

Q: (c) A \ B = A \ (An B). (d) A = (ANB) U (A \ B).

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Q: Suppose A, B, C are sets. Prove that (AUB) – C = (A − C) U (B − C)

A: A∪B-C=A-C∪B-C

Q: Prove: For all sets A, B and C, An (B-C) = (ANB) - (ANC).

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Q: For the poset, R = ( { 1, 2, 3, 5, 10, 15, 20, 25, 30, 35, 50, 70 }, | ):   Draw the Hasse digrams…

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Q: (m) W ) Given A, Be {sets}, V AC B, A – B= A.

A: Given: A,B∈sets and A⊂B since A⊂B⇒A-B=ϕ we have to prove A-B=A So, these will happen when A=ϕ So,…

Q: Find the intersection of the sets. {w, y, z}∩∅

A: Given, w,y,z∩∅we have to find intersection of the sets.

Q: If A = {1} and B = {1, 2, 3, 4, 5} , then which of the following is(are) true? Choose one answer and…

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